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More About This Title Statistics and Probability with Applications for Engineers and Scientists
English
Introducing the tools of statisticsand probability from the ground up
An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences.
Unique among books of this kind, Statistics and Probability with Applications for Engineers andScientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab® and Microsoft® Office Excel® to analyze various data sets. The book also features:
• Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices
• A clear presentation of nonparametric methods and simple and multiple linear regression methods, as well as a brief discussion on logistic regression method
• Comprehensive guidance on the design of experiments, including randomized block designs, one- and two-way layout designs, Latin square designs, random effects and mixed effects models, factorial and fractional factorial designs, and response surface methodology
• A companion website containing data sets for Minitab and Microsoft Office Excel, as well as JMP ® routines and results
Assuming no background in probability and statistics, Statistics and Probability with Applications for Engineers and Scientists features a unique, yet tried-and-true, approach that is ideal for all undergraduate students as well as statistical practitioners who analyze and illustrate real-world data in engineering and the natural sciences.
English
BHISHAM C. GUPTA, PhD, is Professor in the Department of Mathematics and Statistics at the University of Southern Maine. Dr. Gupta has written four books and more than thirty articles.
IRWIN GUTTMAN, PhD, is Professor Emeritus of Statistics in the Department of Mathematics at the State University of New York at Buffalo and Department of Statistics at the University of Toronto, Canada. Dr. Guttman has written five books and over 140 articles.
English
Preface xvii
Chapter 1 | Introduction 1
1.1 Designed Experiment 2
1.1.1 Motivation for the Study 2
1.1.2 Investigation 2
1.1.3 Changing Criteria 2
1.1.4 A Summary of the Various Phases of the Investigation 3
1.2 A Survey 5
1.3 An Observational Study 6
1.4 A Set of Historical Data 6
1.5 A Brief Description of What is Covered in This Book 6
PART I
Chapter 2 | Describing Data Graphically and Numerically 11
2.1 Getting Started with Statistics 12
2.1.1 What Is Statistics? 12
2.1.2 Population and Sample in a Statistical Study 12
2.2 Classification of Various Types of Data 15
2.2.1 Nominal Data 15
2.2.2 Ordinal Data 16
2.2.3 Interval Data 16
2.2.4 Ratio Data 16
2.3 Frequency Distribution Tables for Qualitative and Quantitative Data 17
2.3.1 Qualitative Data 17
2.3.2 Quantitative Data 20
2.4 Graphical Description of Qualitative and Quantitative Data 25
2.4.1 Dot Plot 25
2.4.2 Pie Chart 25
2.4.3 Bar Chart 27
2.4.4 Histograms 30
2.4.5 Line Graph 35
2.4.6 Stem-and-Leaf Plot 37
2.5 Numerical Measures of Quantitative Data 41
2.5.1 Measures of Centrality 42
2.5.2 Measures of Dispersion 46
2.6 Numerical Measures of Grouped Data 55
2.6.1 Mean of a Grouped Data 56
2.6.2 Median of a Grouped Data 56
2.6.3 Mode of a Grouped Data 57
2.6.4 Variance of a Grouped Data 57
2.7 Measures of Relative Position 59
2.7.1 Percentiles 59
2.7.2 Quartiles 60
2.7.3 Interquartile Range 60
2.7.4 Coefficient of Variation 61
2.8 Box-Whisker Plot 62
2.8.1 Construction of a Box Plot 62
2.8.2 How to Use the Box Plot 63
2.9 Measures of Association 68
2.10 Case Studies 71
2.11 Using JMP1 73
Review Practice Problems 73
Chapter 3 | Elements of Probability 83
3.1 Introduction 84
3.2 Random Experiments, Sample Spaces, and Events 84
3.2.1 Random Experiments and Sample Spaces 84
3.2.2 Events 85
3.3 Concepts of Probability 88
3.4 Techniques of Counting Sample Points 93
3.4.1 Tree Diagram 93
3.4.2 Permutations 94
3.4.3 Combinations 95
3.4.4 Arrangements of n Objects Involving Several Kinds of Objects 96
3.5 Conditional Probability 98
3.6 Bayes’s Theorem 100
3.7 Introducing Random Variables 104
Review Practice Problems 105
Chapter 4 | Discrete Random Variables and Some Important Discrete
Probability Distributions 111
4.1 Graphical Descriptions of Discrete Distributions 112
4.2 Mean and Variance of a Discrete Random Variable 113
4.2.1 Expected Value of Discrete Random Variables and Their Functions 113
4.2.2 The Moment-Generating Function–Expected Value of a Special Function of X 115
4.3 The Discrete Uniform Distribution 117
4.4 The Hypergeometric Distribution 119
4.5 The Bernoulli Distribution 122
4.6 The Binomial Distribution 123
4.7 The Multinomial Distribution 126
4.8 The Poisson Distribution 128
4.8.1 Definition and Properties of the Poisson Distribution 128
4.8.2 Poisson Process 128
4.8.3 Poisson Distribution as a Limiting Form of the Binomial 128
4.9 The Negative Binomial Distribution 132
4.10 Some Derivations and Proofs (Optional) 135
4.11 A Case Study 135
4.12 Using JMP 135
Review Practice Problems 136
Chapter 5 | Continuous Random Variables and Some Important Continuous Probability Distributions 143
5.1 Continuous Random Variables 144
5.2 Mean and Variance of Continuous Random Variables 146
5.2.1 Expected Value of Continuous Random Variables and Their Function 146
5.2.2 The Moment-Generating Function–Expected Value of a Special Function of X 149
5.3 Chebychev’s Inequality 151
5.4 The Uniform Distribution 152
5.4.1 Definition and Properties 152
5.4.2 Mean and Standard Deviation of the Uniform Distribution 155
5.5 The Normal Distribution 157
5.5.1 Definition and Properties 157
5.5.2 The Standard Normal Distribution 158
5.5.3 The Moment-Generating Function of the Normal Distribution 164
5.6 Distribution of Linear Combination of Independent Normal Variables 165
5.7 Approximation of the Binomial and Poisson Distribution by the Normal Distribution 169
5.7.1 Approximation of the Binomial Distribution by the Normal Distribution 169
5.7.2 Approximation of the Poisson Distribution by the Normal Distribution 171
5.8 A Test of Normality 171
5.9 Probability Models Commonly Used in Reliability Theory 175
5.9.1 The Lognormal Distribution 176
5.9.2 The Exponential Distribution 180
5.9.3 The Gamma Distribution 184
5.9.4 The Weibull Distribution 187
5.10 A Case Study 191
5.11 Using JMP 192
Review Practice Problems 192
Chapter 6 | Distribution of Functions of Random Variables 199
6.1 Introduction 200
6.2 Distribution Functions of Two Random Variables 200
6.2.1 Case of Two Discrete Random Variables 200
6.2.2 Case of Two Continuous Random Variables 202
6.2.3 The Mean Value and Variance of Functions of Two Random Variables 204
6.2.4 Conditional Distributions 206
6.2.5 Correlation between Two Random Variables 208
6.2.6 Bivariate Normal Distribution 211
6.3 Extension to Several Random Variables 214
6.4 The Moment-Generating Function Revisited 214
Review Practice Problems 218
Chapter 7 | Sampling Distributions 223
7.1 Random Sampling 224
7.1.1 Random Sampling from an Infinite Population 224
7.1.2 Random Sampling from a Finite Population 225
7.2 The Sampling Distribution of the Mean 228
7.2.1 Normal Sampled Population 228
7.2.2 Nonnormal Sampled Population 228
7.2.3 The Central Limit Theorem 228
7.3 Sampling from a Normal Population 234
7.3.1 The Chi-Square Distribution 234
7.3.2 The Student t-Distribution 240
7.3.3 Snedecor’s F-Distribution 244
7.4 Order Statistics 247
7.5 Using JMP 247
Review Practice Problems 247
Chapter 8 | Estimation of Population Parameters 251
8.1 Introduction 252
8.2 Point Estimators for the Population Mean and Variance 252
8.2.1 Properties of Point Estimators 253
8.2.2 Methods of Finding Point Estimators 256
8.3 Interval Estimators for the Mean m of a Normal Population 262
8.3.1 s2 Known 262
8.3.2 s2 Unknown 264
8.3.3 Sample Size Is Large 266
8.4 Interval Estimators for the Difference of Means of Two Normal Populations 272
8.4.1 Variances Are Known 272
8.4.2 Variances Are Unknown 273
8.5 Interval Estimators for the Variance of a Normal Population 280
8.6 Interval Estimator for the Ratio of Variances of Two Normal Populations 284
8.7 Point and Interval Estimators for the Parameters of Binomial Populations 288
8.7.1 One Binomial Population 288
8.7.2 Two Binomial Populations 290
8.8 Determination of Sample Size 294
8.8.1 One Population Mean 294
8.8.2 Difference of Two Population Means 295
8.8.3 One Population Proportion 296
8.8.4 Difference of Two Population Proportions 296
8.9 Some Supplemental Information 298
8.10 A Case Study 298
8.11 Using JMP 299
Review Practice Problems 299
Chapter 9 | Hypothesis Testing 307
9.1 Introduction 308
9.2 Basic Concepts of Testing a Statistical Hypothesis 308
9.2.1 Hypothesis Formulation 308
9.2.2 Risk Assessment 310
9.3 Tests Concerning the Mean of a Normal Population Having Known Variance 312
9.3.1 Case of a One-Tail (Left-Sided) Test 312
9.3.2 Case of a One-Tail (Right-Sided) Test 316
9.3.3 Case of a Two-Tail Test 317
9.4 Tests Concerning the Mean of a Normal Population Having Unknown Variance 324
9.4.1 Case of a Left-Tail Test 324
9.4.2 Case of a Right-Tail Test 326
9.4.3 The Two-Tail Case 326
9.5 Large Sample Theory 330
9.6 Tests Concerning the Difference of Means of Two Populations Having Distributions with Known Variances 332
9.6.1 The Left-Tail Test 332
9.6.2 The Right-Tail Test 333
9.6.3 The Two-Tail Test 334
9.7 Tests Concerning the Difference of Means of Two Populations Having Normal Distributions with Unknown Variances 339
9.7.1 Two Population Variances Are Equal 339
9.7.2 Two Population Variances Are Unequal 342
9.7.3 The Paired t-Test 344
9.8 Testing Population Proportions 349
9.8.1 Test Concerning One Population Proportion 349
9.8.2 Test Concerning the Difference between Two Population Proportions 351
9.9 Tests Concerning the Variance of a Normal Population 355
9.10 Tests Concerning the Ratio of Variances of Two Normal Populations 358
9.11 Testing of Statistical Hypotheses Using Confidence Intervals 362
9.12 Sequential Tests of Hypotheses 367
9.12.1 A One-Tail Sequential Testing Procedure 367
9.12.2 A Two-Tail Sequential Testing Procedure 371
9.13 Case Studies 374
9.14 Using JMP 375
Review Practice Problems 375
PART II
Chapter 10 | Elements of Reliability Theory 389
10.1 The Reliability Function 390
10.1.1 The Hazard Rate Function 391
10.1.2 Employing the Hazard Function 398
10.2 Estimation: Exponential Distribution 399
10.3 Hypothesis Testing: Exponential Distribution 406
10.4 Estimation: Weibull Distribution 407
10.5 Case Studies 414
10.6 Using JMP 416
Review Practice Problems 416
Chapter 11 | Statistical Quality Control—Phase I Control Charts 419
11.1 Basic Concepts of Quality and Its Benefits 420
11.2 What a Process Is and Some Valuable Tools 420
11.2.1 Check Sheet 422
11.2.2 Pareto Chart 422
11.2.3 Cause-and-Effect (Fishbone or Ishikawa) Diagram 425
11.2.4 Defect Concentration Diagram 427
11.3 Common and Assignable Causes 427
11.3.1 Process Evaluation 427
11.3.2 Action on the Process 428
11.3.3 Action on Output 428
11.3.4 Variation 428
11.4 Control Charts 429
11.4.1 Preparation for Use of Control Charts 430
11.4.2 Benefits of a Control Chart 431
11.4.3 Control Limits Versus Specification Limits 433
11.5 Control Charts for Variables 434
11.5.1 Shewhart X and R Control Charts 434
11.5.2 Shewhart X and R Control Charts When Process Mean m and Process Standard Deviation s Are Known 440
11.5.3 Shewhart X and S Control Charts 441
11.6 Control Charts for Attributes 448
11.6.1 The p Chart: Control Chart for the Fraction of Nonconforming Units 449
11.6.2 The p Chart: Control Chart for the Fraction Nonconforming with Variable Sample Sizes 454
11.6.3 The np Control Chart: Control Chart for the Number of Nonconforming Units 456
11.6.4 The c Control Chart 458
11.6.5 The u Control Chart 461
11.7 Process Capability 468
11.8 Case Studies 470
11.9 Using JMP 472
Review Practice Problems 472
Chapter 12 | Statistical Quality Control—Phase II Control Charts 479
12.1 Introduction 480
12.2 Basic Concepts of CUSUM Control Chart 480
12.3 Designing a CUSUM Control Chart 483
12.3.1 Two-Sided CUSUM Control Chart Using a Numerical Procedure 484
12.3.2 The Fast Initial Response (FIR) Feature for CUSUM Control Chart 489
12.3.3 The Combined Shewhart–CUSUM Control Chart 492
12.3.4 The CUSUM Control Chart for Controlling Process Variability 493
12.4 The Moving Average (MA) Control Chart 495
12.5 The Exponentially Weighted Moving Average (EWMA) Control Chart 499
12.6 Case Studies 504
12.7 Using JMP 505
Review Practice Problems 506
Chapter 13 | Analysis of Categorical Data 509
13.1 Introduction 509
13.2 The Chi-Square Goodness-of-Fit Test 510
13.3 Contingency Tables 517
13.3.1 The 2 2 Case Parameters Known 517
13.3.2 The 2 2 Case with Unknown Parameters 519
13.3.3 The r s Contingency Table 521
13.4 Chi-Square Test for Homogeneity 525
13.5 Comments on the Distribution of the Lack-of-Fit Statistics 528
13.6 Case Studies 529
Review Practice Problems 531
Chapter 14 | Nonparametric Tests 537
14.1 Introduction 537
14.2 The Sign Test 538
14.2.1 One-Sample Test 538
14.2.2 The Wilcoxon Signed-Rank Test 541
14.2.3 Two-Sample Test 543
14.3 Mann–Whitney (Wilcoxon) W Test for Two Samples 548
14.4 Runs Test 551
14.4.1 Runs Above and Below the Median 551
14.4.2 The Wald–Wolfowitz Run Test 553
14.5 Spearman Rank Correlation 556
14.6 Using JMP 559
Review Practice Problems 559
Chapter 15 | Simple Linear Regression Analysis 565
15.1 Introduction 566
15.2 Fitting the Simple Linear Regression Model 567
15.2.1 Simple Linear Regression Model 567
15.2.2 Fitting a Straight Line by Least Squares 569
15.2.3 Sampling Distribution of the Estimators of Regression Coefficients 573
15.3 Unbiased Estimator of s2 578
15.4 Further Inferences Concerning Regression Coefficients (b0, b1), E(Y), and Y 580
15.4.1 Confidence Interval for b1 with Confidence Coefficient (1 a) 580
15.4.2 Confidence Interval for b0 with Confidence Coefficient (1a) 581
15.4.3 Confidence Interval for E(YjX) with Confidence Coefficient (1 a) 582
15.4.4 Prediction Interval for a Future Observation Y with Confidence Coefficient (1 a) 585
15.5 Tests of Hypotheses for b0 and b1 590
15.5.1 Test of Hypotheses for b1 590
15.5.2 Test of Hypotheses for b0 590
15.6 Analysis of Variance Approach to Simple Linear Regression Analysis 596
15.7 Residual Analysis 601
15.8 Transformations 609
15.9 Inference About r 615
15.10 A Case Study 618
15.11 Using JMP 619
Review Practice Problems 619
Chapter 16 | Multiple Linear Regression Analysis 627
16.1 Introduction 628
16.2 Multiple Linear Regression Models 628
16.3 Estimation of Regression Coefficients 632
16.3.1 Estimation of Regression Coefficients Using Matrix Notation 633
16.3.2 Properties of the Least-Squares Estimators 635
16.3.3 The Analysis of Variance Table 636
16.3.4 More Inferences about Regression Coefficients 639
16.4 Multiple Linear Regression Model Using Quantitative and Qualitative Predictor Variables 646
16.4.1 Single Qualitative Variable with Two Categories 646
16.4.2 Single Qualitative Variable with Three or More Categories 647
16.5 Standardized Regression Coefficients 658
16.5.1 Multicollinearity 660
16.5.2 Consequences of Multicollinearity 661
16.6 Building Regression Type Prediction Models 662
16.6.1 First Variable to Enter into the Model 662
16.7 Residual Analysis and Certain Criteria for Model Selection 665
16.7.1 Residual Analysis 665
16.7.2 Certain Criteria for Model Selection 667
16.8 Logistic Regression 672
16.9 Case Studies 676
16.10 Using JMP 677
Review Practice Problems 678
Chapter 17 | Analysis of Variance 685
17.1 Introduction 686
17.2 The Design Models 686
17.2.1 Estimable Parameters 686
17.2.2 Estimable Functions 688
17.3 One-Way Experimental Layouts 689
17.3.1 The Model and Its Analysis 689
17.3.2 Confidence Intervals for Treatment Means 695
17.3.3 Multiple Comparisons 700
17.3.4 Determination of Sample Size 706
17.3.5 The Kruskal–Wallis Test for One-Way Layouts (Nonparametric Method) 707
17.4 Randomized Complete Block Designs 710
17.4.1 The Friedman Fr-Test for Randomized Complete Block Design (Nonparametric Method) 718
17.4.2 Experiments with One Missing Observation in an RCB-Design Experiment 719
17.4.3 Experiments with Several Missing Observations in an RCB-Design Experiment 719
17.5 Two-Way Experimental Layouts 722
17.5.1 Two-Way Experimental Layouts with One Observation per Cell 724
17.5.2 Two-Way Experimental Layouts with r>1 Observations per Cell 725
17.5.3 Blocking in Two-Way Experimental Layouts 734
17.5.4 Extending Two-Way Experimental Designs to n-Way Experimental Layouts 734
17.6 Latin Square Designs 736
17.7 Random-Effects and Mixed-Effects Models 742
17.7.1 Random-Effects Model 742
17.7.2 Mixed-Effects Model 744
17.7.3 Nested (Hierarchical) Designs 746
17.8 A Case Study 752
17.9 Using JMP 753
Review Practice Problems 753
Chapter 18 | The 2k Factorial Designs 765
18.1 Introduction 766
18.2 The Factorial Designs 766
18.3 The 2k Factorial Design 768
18.4 Unreplicated 2k Factorial Designs 776
18.5 Blocking in the 2k Factorial Design 782
18.5.1 Confounding in the 2k Factorial Design 783
18.5.2 Yates’s Algorithm for the 2k Factorial Designs 788
18.6 The 2k Fractional Factorial Designs 790
18.6.1 One-half Replicate of a 2k Factorial Design 790
18.6.2 One-quarter Replicate of a 2k Factorial Design 795
18.7 Case Studies 799
18.8 Using JMP 801
Review Practice Problems 801
Chapter 19 | Response Surfaces
This chapter is not included in text, but is available for download via the book’s website: www.wiley.com/go/statsforengineers
Appendices 807
Appendix A | Statistical Tables 809
Appendix B | Answers to Selected Problems 845
Appendix C | Bibliography 863
Index 867
English
“Considering the size and wealth of information that the book is providing for a one- or two-semester undergraduate course sequence, it is indeed reasonably priced and should be a strong candidate for serious consideration of a softcover edition in the course of time.” (Journal of Statistical Theory and Practice, 10 February 2014)
